Multivariable calculus and vector analysis
A set of on-line readings
Beta Math ML version
Introduction
Topics
By lecture
Complete list
1. Geometry in higher dimensions
1a. Preliminaries
1b. Lines and planes
1c. Matrices
1d. Visualizing functions in higher dimensions
2. Differential Calculus
2a. The partial derivative
2b. The derivative and differentiability
2c. The chain rule, directional derivative and gradient
2d. Applications of differential calculus
3. Integral calculus
3a. Double integrals
3b. Triple Integrals
3c. Changing variables
4. Vector calculus
4a. Vector field basics
4b. Parametrized curves
4c. Parametrized surfaces
4d. Path integrals and line integrals
4e. Surface integrals
5. The fundamental theorems of vector calculus
5a. Green's theorem
5b. The theorem for conservative vector fields
5c. Stokes' theorem
5d. The divergence theorem
6. Review material